Fractional polynomial function in stochastic response surface method for reliability analysis

Abstract

The explicit polynomial function can replace the actual limit state function for failure probability. In this study, the fractional order is introduced to an extended family of polynomial functions to guarantee a smooth relationship between the sample data and polynomial expression. The fractional polynomial method is proposed to establish the function and analyze the system’s reliability accurately and flexibly. Integer, fractional, positive, and negative orders are considered. The scope of orders, constraint conditions, and sampling method are investigated under different conditions of the proposed method. Furthermore, the calculation process for the fractional polynomial method when the approach is applied to a multivariable system is examined, and engineering examples are provided to illustrate the application of the proposed method. The fractional polynomial function can describe system performance and reliability with few terms and high accuracy. The results calculated by the proposed method agree with those from Monte Carlo simulation.